Introduction to Computer Engineering

WEEK-6CODING SYSTEMS

Assoc. Prof. Dr. Ahmet Turan ÖZCERİT

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The necessity and advantages of coding

The variety of coding systems

CODING SYSTEMS

You will learn:

Fundamentals of Coding Systems

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Coding can be defined as the integrity of strict rules between two clusters

In other words, representing any member of a cluster by a code

The advantage of coding

The simplicity of arithmetic operations

Helps to discover errors

Helps to recover from errors

Better performance for memory operations

Better understanding of data operations

Fundamentals of Coding Systems

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Numeric Codes

1,2,3,4,5,6….

Examples: BCD, 8 4 -2 -1, 2 4 2 1, +3Code, Gray and Parity

Alphanumeric Codes

1,2,3,A,B,C,+,%,&,/, (, ) ……

Examples: ASCII, Unicode

Decimal to BCD Conversion

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BCD Coding : Binary Coded Decimal

The decimal numbers are represented as 4-bit binary numbers

Digit BCD Code

0 0000

1 0001

2 0010

…. …..

7 0111

8 1000

9 1001

Examples BCD Code

10 0001 0000

23 0010 0011

122 0001 0010 0010

87 1000 0111

234 0010 0011 0100

897 1000 1001 0111

100 0001 0000 0000

BCD to Decimal Conversion

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Example-1: Convert (1001 0011 0110)BCD into decimal

1001 -> 9, 0011-> 3, 0110-> 6

Example-2: Convert (0001 1000 0101 0100)BCD into decimal

0001 -> 1, 1000-> 8, 0101-> 5, 0100->4

8 4 -2 -1 Coding (self complementary code)

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8 4 -2 -1 23 22 -21 -20

Decimal 8 4 -2 -1 code

0 0000

1 0111

2 0110

3 0101

4 0100

5 1011

6 1010

7 1001

8 1000

9 1111

ExamplesDecimal

8 4 -2 -1code

275 0110 1001 1011

23 0110 0101

122 0111 0110 0110

897 1000 1111 1001

2 4 2 1 Coding(self complementary code)

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Decimal 2 4 2 1 code

0 0000

1 0001

2 0010

3 0011

4 0100

5 1011

6 1100

7 1101

8 1110

9 1111

ExamplesDecimal

2 4 2 1 code

275 0110 1001 1011

23 0110 0101

122 0111 0110 0110

897 1000 1111 1001

+3 Code (self complementary code)

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The primary advantage of +3 coding over non-biased coding is that a decimal number can be nines' complemented (for subtraction) as easily as a binary number can be ones' complemented; just invert all bits. In addition, when the sum of two +3 digits is greater than 9, the carry bit of a four bit adder will be set high. This works because, when adding two numbers that are greater than or equal to zero, an "excess" value of six results in the sum. Since a four bit integer can only hold values 0 to 15, an excess of six means that any sum over nine will overflow.

https://www.youtube.com/watch?v=MXGZ4wXM7_M

0: 00111: 01002: 01013: 01104: 01115: 10006: 10017: 10108: 10119: 1100

Gray Code

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Gray coding has no radix weight

Gray code cannot be used in arithmetic

operations

It reduces error in control signals since

it is based on columns

Gray code can be converted easily into

binary and vice versa

Converting Binary code into Gray

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Converting Gray code into Binary

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Gray code use

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Gray code use

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0 0

1

0 0 00 1

0 0

1

1

1 0 1

1 1 0 1 1 1

1 0 0

sensors

Binary coded: 111 110 000

0 0

0

1 1 10 1

0 0

0

1

1 0 1

0 1 1 1 0 0

1 1 0

mis-aligned sensors

1 0

1

1 1 10 0

0 1

0

0

0 1 0

0 0 1 0 1 1

1 1 0

mis-aligned sensors

Gray coded: 111 101

ALPHANUMERIC CODES

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• Computers also handle textual data.• Character set frequently used:

alphabets: ‘A’ … ‘Z’, ‘a’ … ‘z’digits: ‘0’ … ‘9’special symbols: ‘$’, ‘.’, ‘@’, ‘*’, etc.non-printable: NULL, BELL, CR, etc.

• Examples– ASCII (8 bits), Unicode (8-bit, 16-bit, and 32-bit)

ALPHANUMERIC CODES

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ASCII American Standard Code for Information Interchange 7 bits, plus a parity bit for error detection Odd or even parity 8-bit extended ASCII: code pages for different languages

MSBsLSBs 000 001 010 011 100 101 110 1110000 NUL DLE SP 0 @ P ` p0001 SOH DC1 ! 1 A Q a q0010 STX DC2 “ 2 B R b r0011 ETX DC3 # 3 C S c s0100 EOT DC4 $ 4 D T d t0101 ENQ NAK % 5 E U e u0110 ACK SYN & 6 F V f v0111 BEL ETB ‘ 7 G W g w1000 BS CAN ( 8 H X h x1001 HT EM ) 9 I Y i y1010 LF SUB * : J Z j z1011 VT ESC + ; K [ k {1100 FF FS , < L \ l |1101 CR GS - = M ] m }1110 O RS . > N ^ n ~1111 SI US / ? O _ o DEL

ERROR DETECTION

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• Parity bit– Even parity: additional bit

added to make total number of 1’s even.

– Odd parity: additional bit added to make total number of 1’s odd.

• Example of odd parity on ASCII values.

Character ASCII Code0 0110000 11 0110001 0

. . . . . .9 0111001 1: 0111010 1A 1000001 1B 1000010 1

. . . . . .Z 1011010 1[ 1011011 0\ 1011100 1

Parity bits

ERROR DETECTION

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• Parity bit can detect odd number of errors but not even number of errors.– Example: Assume odd parity,

• 10011 10001 (detected)• 10011 10101 (not detected)

• Parity bits can also be applied to a block of data.

0110 10001 01011 01111 11001 10101 0 Column-wise parity

Row-wise parity

QUESTIONS

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